Obesity percentage

Question

The formula  models the percent of U.S. adults who are considered obese by federal guidelines, where  is the number of years after 1984, and  is the percent of obese adults. According to this formula, in what year was the obesity rate 19.9 percent? 

In this equation,  is already converted from a decimal, so, for example, a 19.9 percent obesity rate would correspond to 19.9.

Answer 1

Hi Jeslyn! I would be happy to help you with this problem.

First we are going to start but plugging in what we have been given into the equation. The problem gives us y=19.9, so we will substitute that in for y in the equation like this,

19.9=3√x+12

The goal is to isolate x in order to solve for it so the first step will be to subtract 12 from both sides of the equation to get this,

7.9=3√x

Now we want to get the √x by itself by dividing both sides of the equation by 3 to get this,

2.63=√x

The last step to solve for x is to square both sides so that we can get rid of the square root, doing that will give us this,

6.93=x

The equation is asking us for the year in which the percent of obese adults is 19.9%, which was y, and x gives us the number of years after 1984.

All you have to do is add what you got for x to 1984. I'm assuming it would want you to round to the nearest year, so it would be 1991. Hope this helps! :)